All should be doable within the parameters you listed.
I built a 7' x 14' cabin on a 20' long single axle boat trailer.
I made the standard full size bed into a "murphy" configuration to save floor space, and have a seating/dining area there when the bed is folded up.
I have 8 linear foot of kitchen counter/cabinets with a sink, propane oven and range, plus an additional 2 linear foot for a free standing refrigerator with a microwave oven on top. I also have a combination toilet / shower and 7 linear foot of floor to ceiling closet space, 18" deep. There is additional storage under the benches below the bed for folded clothing and my computer, scanner and printer. I also have a wall mounted TV/DVD player.
I framed mostly with 2 x 3 studs on edge, finished the interior with 5/16" bead board paneling, and the entire exterior is 26 and 28 gauge steel which would weight about 50% more than aluminum but less than 5/8" plywood. Total weight is 2800#. The walls are insulated with 1-1/2" polyurethane board, the ceiling/roof is 2-1/2", and the floor varies from 3" to 4."
Interior height is 72" in the center and exterior height 96" to the peak of the gable roof.
It is fully self contained with fresh, gray and black water tanks, 12V DC pump, propane water heater, 12V DC outlets and LED lighting, plus 110V AC outlets for the large appliances. I used a WFCO converter (not everyone here is a fan but mine has been trouble free), Interstate AGM battery, and a 2000W inverter.
I have both a propane heater and an electric "faux" fireplace but last winter only used a sleeping bag and two small dogs,
The 6' tongue has tool storage, a cover for the air conditioner, 1800 watt generator, and space for either 2 bicycles or one motorbike (Yamaha TW200) and room for a little bit of firewood.
See my "Log Cabin" build thread.